Question

Solve.

`2\pi \sqrt{ ( (9)/(2) )/(32) }`

Answer 1

`\bf 2\pi \sqrt{\cfrac{\quad (9)/(2)\quad }{32}}\implies 2\pi \sqrt{\cfrac{\quad (9)/(2)\quad }{(32)/(1)}}\implies 2\pi \sqrt{\cfrac{9}{2}\cdot \cfrac{1}{32}}\implies 2\pi \sqrt{\cfrac{9}{64}} \\\\\\ 2\pi \sqrt{\cfrac{3^2}{8^2}}\implies 2\pi \cdot \cfrac{3}{8}\implies \cfrac{3\pi }{4}`